Wednesday, June 19, 2024

# What Does Stem And Leaf Plot Mean In Math

## How To Split A Stem And Leaf Plot

Stem-and-leaf plots | Applying mathematical reasoning | Pre-Algebra | Khan Academy

The split stem and leaf plot separates each stem into many stems based on its frequency. We place the smaller leaves on the first part of the split stem and the larger leaves on the subsequent stems.

For example, let’s consider a set of data that includes the scores of 7 students in their math test.

78, 82, 82, 90, 94, 81, 72Data in ascending order 72, 78, 81, 82, 82, 90, 94

Stem and Leaf Plot:

Split Stem And Leaf Plot

Stem
9 4

Thus, the split stem and leaf plot is an ordinary stem and leaf plot with each instance of the stem-leaf shown separately. It represents the stem section as many entries like how it appears in the data values.

## Example : Answering Questions Using A Stem And Leaf Diagram

The stem and leaf diagram below shows the ages of a group of people at a party.

How many people are there in the group?

Count all the numbers in the leaf, so the answer is 10 people.

What age is the youngest member of the group?

The first number in the leaf is the smallest value, so the answer is 35 years old.

What age is the oldest member of the group?

The last number in the leaf is the largest value, so the answer is 56 years old.

How many people are under \bf ?

Count all the values in the leaf that are less than 45, so the answer is 5 people.

How many people are \bf and over?

Count all the people in the leaf that are 45 and above, so the answer is 5 people.

## How To Read A Stem And Leaf Plot

As we have learnt, a stem and leaf plot is used for the schematic representation of data. So, how do we read a stem and leaf plot diagram if we have one? Let us understand this by an example.

Suppose we are given the following stem and leaf plot.

 Stem 0 8

What is the interpretation of this plot? Let us find out.

We have learnt that the stem of a stem and the leaf plot represents the tens while the leaves of the plot represent the ones. Using this characteristic of the stem and leaf plot, we can identify the following from the above plot

Minimum Value Notice that the minimum value of the stem is 14. Also, the leaves against this number 14 are two numbers, 4 and 7. This means that stem 14 and the leaves 4 and 7 represent the numbers 144 and 147 respectively. Since these will be the lowest values in the stem and leaf plot, therefore the minimum value of the data that is represented by this stem and leaf plot is 144.

Now, let us look at the maximum value of the data represented by this stem and leaf plot.

Maximum Value Notice that the maximum value of the stem is 18. Also, the leaves against this number 18 are two numbers, 0 and 8. This means that the stem 18 and the leaves 0 and 8 represent the numbers 180 and 188 respectively. Since these will be the largest values in the stem and leaf plot, therefore the maximum value of the data that is represented by this stem and leaf plot is 188.

Can we also find the mode using the stem and leaf plot? Let us find out.

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## How To Construct Stem And Leaf Plot

Follow the steps for constructing a stem and leaf plot.

• Step 1: Look at the data and find the number of digits. Classify them as 2 or 3 digit numbers.
• Step 2: Fix the stem and leaf plot key. For example, 3 I 5 = 35, and 15 I 2 is 152.
• Step 3: Identify the first digits as stems and the last digit as leaves.
• Step 4: Determine the range of the data, i.e. the lowest and the highest values among the data.
• Step 5: Draw a vertical line. Place the stem on the left column and the leaf on the right column.
• Step 6: List the stems in the stems column. Arrange it in ascending order starting from the lowest to the top.
• Step 7: Plot the leaves in the column against the stem from lowest to the highest horizontally.

Important Notes

Given below are some important notes related to stem and leaf plots. Have a look!

• If we plot data using stem and leaf and place it alongside the new data, we might be able to see a correlation between both the data and the frequency distribution of data.
• The stem and leaf plot key for three-digit numbers is represented as two digits in the stem and one digit in the leaf. For example, 45 | 6 = 456
• The mean, median, and mode of the given data can easily be calculated using stem and leaf plots.

## How To Interpret A Stem

Suppose we have the following stem and leaf plot that shows the number of ice cream cones that Marie sold at her ice cream shop during each of the past 14 days:

7 | 3 3 3 7 98 | 4 5 8 89 | 1 2 5 8 9

Question: What is the most cones that Marie sold on any given day?

7 | 3 3 3 7 98 | 4 5 8 89 | 1 2 5 8 9

Question: During how many days did Marie sell more than 80 cones?

7 | 3 3 3 7 98 | 4 5 8 89 | 1 2 5 8 9

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## Usage Of Stem And Leaf Plots

As mentioned above, Stem and Leaf plots are widely being used in mathematics and research. This is because it splits the data in a smart way and enhances its ability. In addition to this, it has extensive use in exploratory research as well. Other than this, the Stem and Leaf plots are also being used in:

• The plot or diagram is being used to classify discrete or continuous variables.
• In addition to this, it organizes data on the point of its collection.
• Other than this, it looks like a bar graph and performs similar functions.
• They are also being used in a classroom setting where the instructor wants to plot the scores of different students.

## What Is The Difference Between A Stem And Leaf Plot And A Histogram

A stem and leaf plot is a way to plot data values where the data values are split into stems and leaves. Under stems, we write the starting digit or digits and in leaf, we write the end digit of value whereas a histogram is a graphical representation of data using rectangular bars to represent data values.

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## Example 5 Splitting Stems Using Decimal Values

The weights of 30 students were measured and recorded as follows:

59.2, 61.5, 62.3, 61.4, 60.9, 59.8, 60.5, 59.0, 61.1, 60.7, 61.6, 56.3, 61.9, 65.7, 60.4, 58.9, 59.0, 61.2, 62.1, 61.4, 58.4, 60.8, 60.2, 62.7, 60.0, 59.3, 61.9, 61.7, 58.4, 62.2

Prepare an ordered stem and leaf plot for the data. Briefly comment on what the analysis shows.

In this case, the stems will be the whole number values and the leaves will be the decimal values. The data range from 56.3 to 65.7, so the stems should start at 56 and finish at 65.

Table 8. Weights of 30 students

Stem
65 7

In this example, it was not necessary to split stems because the leaves are not crowded on too few stems nor was it necessary to round the values, since the range of values is not large. This stem and leaf plot reveals that the group with the highest number of observations recorded is the 61.0 to 61.9 group.

## Elements Of A Good Stem And Leaf Plot

What is a Stem and Leaf Plot & How Does IT Organize Data? *Math for Kids*

A good stem and leaf plot

• shows the first digits of the number as the stem and shows the last digit as the leaf.
• usually uses whole numbers. Anything that has a decimal point is rounded to the nearest whole number. For example, test results, speeds, heights, weights, etc.
• looks like a bar graph when it is turned on its side.
• shows how the data are spreadthat is, highest number, lowest number, most common number and outliers .

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## What Is A Stem And Leaf Plot

The Stem and Leaf plot is a concept in mathematics that makes it more fun. In addition to this, aside from making it more fun, it helps in dealing with loads of data efficiently and effectively. The stem is basically on the left side that displays the first digit. However, the leaf is on the right side. And the main purpose of the leaf is to display the last digits.

#### Want to Know More About it?

The Stem and Leaf plot has made our lives much easier. Such diagrams help us tackle the data smartly. Furthermore, since it spreads the data, it improves its readability. So, one could never miss out on any number while playing with the data.

A stem and leaf plot is a unique table that helps us smartly split the data. For example, 568 and 561 can be split and written like 56 | 8,1. This has improved its readability. Such diagrams have eased inferential and nonparametric statistics.

## Why Stems And Leaves

Lets kick things off with a recap of the basics of making stem-and-leaf plots and a look at why they’re called “stem-and-leaf” plots in the first place. As we’ve learned, a stem-and-leaf plot is really just a two-column table: the first column contains the “stems made up of the first digit of your numerical data, and the second column contains horizontal lists of leaves made from the last digits of your data points. So there are multiple “leaves” for each “stem” of data, just as there are multiple leaves on each branch of a tree get it?

A stem-and-leaf plot is really just a two-column table

To illustrate what this all means in practice, we imagined measuring the widths of a bunch of leaves, all of which were between 7 and 23 cm wide. To make a stem-and-leaf plot of this data, you begin by filling the first column with the stems,” 0, 1, and 2. The stem labeled 0″ is for all the leaves with single digit widths between 0 and 9 cm, the stem labeled 1 is for all the leaves with widths between 10 and 19 cm wide, and the stem labeled 2″ is for all the leaves with widths between 20 and 29 cm wide.

After youve made your stems,” you just have to add the leaves” to your plot. If one of the leaves youve measured has a width of 14 cm, you would write 4 in the second column of the row with 1 in the first column. For a 7 cm wide leaf, you would write 7 in the second column of the row with 0 in the first column. And so on for each leaf in your data set.

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## What Are The Uses Of Stem And Leaf Plots

Effective way to organize the data. A stem and leaf plot looks something like a bar graph .

• Shows data in an organized way,so it can be analyzed easily.
• Organizes data so it easy to compute the median,mode and quartiles.
• Easy to compare different sets of data together at the same time.
• What is a disadvantage of using a stem and leaf plot?

A disadvantage of stem and leaf plots is they are really only useful for small data sets from about 15 to 150 data points. Dot plots are usually more useful for smaller data sets, and for larger data sets a box plot or histogram is used.

## Stem And Leaf Plot With Decimals

We can use stem and leaf plots with the same way we use for whole numbers. The stem and leaf plot key helps us understand how the data is organized on the stem and leaf plot with decimals. For example, stem and leaf plot key 4 I 2 is 4.2. 4 on the stem and 2 on the leaf read as 4.2. The decimal part will show on the leaf side.

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## The Main Advantage Of A Stem And Leaf Plot

The main advantage of a stem and leaf plot is that the data are grouped and all the original data are shown, too. In Example 3 on battery life in the Frequency distribution tables section, the table shows that two observations occurred in the interval from 360 to 369 minutes. However, the table does not tell you what those actual observations are. A stem and leaf plot would show that information. Without a stem and leaf plot, the two values can only be found by searching through all the original dataa tedious task when you have lots of data!

When looking at a data set, each observation may be considered as consisting of two partsa stem and a leaf. To make a stem and leaf plot, each observed value must first be separated into its two parts:

• The stem is the first digit or digits
• The leaf is the final digit of a value
• Each stem can consist of any number of digits but
• Each leaf can have only a single digit.
• stem 0 represents the class interval 0 to 9
• stem 1 represents the class interval 10 to 19 and
• stem 2 represents the class interval 20 to 29.

Usually, a stem and leaf plot is ordered, which simply means that the leaves are arranged in ascending order from left to right. Also, there is no need to separate the leaves with punctuation marks since each leaf is always a single digit.

Using the data from Table 2, we made the ordered stem and leaf plot shown below:

Table 3. Books read in a year by 10 students

Stem

## Stem And Leaf Plot Definition

The Stem and Leaf plot is a way of organizing data into a form that makes it easy to see the frequency of different values. In other words, we can say that a Stem and Leaf Plot is a table in which each data value is split into a stem and a leaf. The stem is the left-hand column that has the tens of digits. The leaves are listed in the right-hand column, showing all the ones digit for each of the tens, the twenties, thirties, and forties.

Remember that Stem and Leaf plots are a pictorial representation of grouped data, but they can also be called a modal representation. Because, by quick visual inspection at the Stem and Leaf plot, we can determine the mode.

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## What Can We Learn From Stem

But the big question is: What can you learn from such a plot? The answer is: Quite a lot. For example, imagine that you want to find the most common leaf width. In other words, you want to find one of the statistical quantities known as the mode or the median of your data set. How can you do it?

One way would be to write out all the values in your data set in a big long list ordered from smallest to largest. Then, to find the median value, you just have to count out and find the value thats right in the middle of the list.

While its also possible to find the mode this way , it’s a bit painful to do. To find the mode using your ordered list, you would have to look through the entire thing and constantly keep track of which number has occurred the most. Its doable, but its a lot to keep track of and it’s not exactly the most convenient thing in the world to do in your head.

What other options do you have?

## Introduction To Stem And Leaf Plots

Stem & Leaf Plots | Probability | Maths | FuseSchool

Statistics need to be often displayed graphically to be able to read the data and analyse it easily. There are several ways to represent statistical data graphically. These include bar graphs, histograms, line graphs, column charts, line charts, pie charts, pivot tables, scatter charts, treemaps, stem and leaf plots, etc.

Displaying statistical data visually or Data visualization is a useful way to provide accessible ways to analyze patterns trends across a large set of data. These are used by data scientists, governments, climatologists, etc to record data and represent it graphically for easier analysis.

Stem and leaf plots are one such way of representing data in an easier and convenient way. Stem and leaf plots have several advantages that make them very handy for the purpose of analyzing large sets of data easily.

A basic understanding of different ways of data visualization comes in handy in all fields. Stem and leaf plots are a method of displaying data horizontally in two columns. They look very simple and can be used to display a huge set of data.

Lastly, any questions that you may have regarding the stem and leaf plots will also be answered. Refer to the official website of Vedantu or download the app for an elaborate and comprehensive explanation.

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## Here Is A Typical Example:

Message from your Math instructor.Results of Exam1 are presentedwith a stem-and-leaf graph.Class Scores:75,8,36,36,55,55,27,83,17,58,55,42,36,50,42,82,27,92,50,42,100,83,27,58,55Your score out of 100 is at the end of this message.All the grades are listed.The scores go from 8 to 100.The Stem-and-leaf is:N = 25   Median = 50Quartiles = 36, 58Decimal point is 1 place to the right of the colon    0 : 8    1 : 7    2 : 777    3 : 666    4 : 222    5 : 00555588    6 :    7 : 5    8 : 233    9 : 2   10 : 0--------------------------------------------------STUDENT NAME             USERID  EX1Brown Charlie            CB1234  55